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Conditional expected sojourn times in insensitive queueing systems and networks

Published online by Cambridge University Press:  01 July 2016

Uwe Jansen
Uwe Jansen*
Affiliation:
Bergakademie Freiberg
*
∗Postal address: Bergakademie Freiberg, Sektion Mathematik, Bernhard-von-Cotta Str. 2, 92 Freiberg (Sachs.), GDR.
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Abstract

We consider queueing systems where the stationary state probabilities are insensitive with respect to the distribution of certain basic random variables such as service requirements, interarrival times, repair times, etc. The conditional expected sojourn times are stated as Radon–Nikodym densities of the stationary distribution at jump points of the queueing system. The conditions are the given values of such basic random variables for which the insensitivity is valid. We use stationary point processes as our main tool. This means that dependences between certain basic random variables are permitted. Conditional expected real service times, conditional mean response times in closed queueing networks, and similar conditional expected values, are dealt with as special cases.

Keywords

INSENSITIVITYMEAN SOJOURN TIMESRADON–NIKODYM DENSITIESSTATIONARY POINT PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 4 , December 1984 , pp. 906 - 919
Copyright
Copyright © Applied Probability Trust 1984 

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